people prefer to bind the event to the parent element
This is referred to as event delegation and is especially useful when you want to trigger the same event handler for multiple elements. Instead of binding an event handler to each those elements, you bind it to a common ancestor and then check from which element the event originated. This works, because events bubble up the DOM tree.
I wonder which is better?
It depends, both approaches have their pros and cons.
Event delegation can be slower, as the event has to bubble up first. You also might have to perform DOM traversal because the event might not originate at the element you test for. For instance, in your example, the li elements might have other children, lets say an a element. To find out whether the clicked a element is a descendant of one of the lis, you have to traverse the ancestors and test them.
On the other hand, binding the handler directly is faster in the sense that the event is processed directly at the element. But if you bind a lot of event handlers and don't do it properly (like in your example) you use more memory than you actually need. Older browsers (I think especially IE) might also perform worse if there are many event handlers.
Also,sometime when handle the drag effect,people always bind the mousemove event to the whole document,why?
The problem is that while dragging an element, the mouse often moves faster than the element and leaves it. If you bind the mousemove event only to the dragged element, whenever the cursor leaves the element, the movement would stop. To avoid this, the event handler is bound to the whole document (for the duration of the dragging) so that the movement is smoothly.